Brouwer's goal gave the Capitals a 2-1 lead with 9:36 left in the second period and Tomas Vokoun stopped 31 shots in halting the Rangers' five-game winning streak.
Semin delivered his eighth and ninth goals of the season, scoring with 6:58 left in the middle period and with 2:35 to go in the third. Alex Ovechkin assisted on both of Semin's goals.
Washington had dropped two in a row.
Brandon Dubinsky produced the only New York goal. It was only the third time in 17 games the Rangers failed to score at least twice.
Martin Biron gave up all four goals on 23 shots.
Millions of Getty images now available for free via embed tool
NBC reportedly holds celebs hostage to Jimmy Fallon's show